# Research on the supply and demand balance mechanism model of city transportation system.

1. IntroductionWith the rapid development of social economy, the urbanization of the city is becoming more and more obvious, the formation and development of city agglomeration have become a symbol and trend of urbanization in our country, so it is important to exert the support function of transportation system to the whole process of city agglomeration development (Haghani, 2003; Fan, 2011; Delgado, 2015). With the continuous increase of traffic demand in city agglomeration, city agglomeration transportation system is facing a severe challenge, the imbalance between supply and demand (Li, 2008; Ju, 2009; Li, 2011). With regard to this problem, a new theoretical mindset should be applied to determine the non-equilibrium depth of supply and demand in the city agglomeration transportation system in order to explore the transition way from non-equilibrium to equilibrium.

At present, the non-equilibrium depth measurement of the supply and demand of city agglomeration transportation system has proved to be competent to analyze and solve the contradiction between supply and demand. Zhang H.M. has proposed the theory and model of non-equilibrium traffic flow with studying the structural characteristics of the model. Shah and Firesz took a further study and summary to the design of the non-equilibrium network. Carey quoted "price" and "quantity" of the non equilibrium theory into the study of the optimal model of equilibrium with dual form. In the aspect of spatial price equilibrium, Nagurney described the state of the commodity market-equilibrium and non-equilibrium, and established the variational inequality model. By analyzing the impact of traffic information on travel route and studying the process of the daily (day-to-day) network flow from a non-equilibrium state to another non-equilibrium state, Ganjalizadeh and David Bernsteinin put forward the idea of unbalanced network design. In domestic, Qiaoyan Shao has built the model of the non-equilibrium based on the time and space resources from a single city, and analyzed the characteristics in the non-equilibrium state (Qiao, 2015). Zhang has studied determination of supply and demand disequilibrium in terms of year, queue length, speed cases (Zhang, 2014). Moreover, Binglin Li has put forward the calculation method of non-equilibrium of supply and demand in the research of single city. Based on the general definition of non-equilibrium depth, Yanyan Li has proposed the non-equilibrium depth of the traffic supply and demand in a general sense (Terry, 2001; Yang, 2011).

In conclusion, most of the current domestic and foreign research tends to study the relationship between supply and demand in a single city or a single transport mode. However, the city agglomeration has become the main carrier of domestic and international competition in the modern transportation system. The measurement of the supply and demand non-equilibrium depth plays a fundamental role in city agglomeration transportation system. Based on the non-equilibrium characteristics of supply greater or less than demand in city agglomeration transportation system, the method to determining the supply and demand non-equilibrium depth is put forward, which aims to provide some ideas and methods for the application of the non-equilibrium in traffic planning as well as a series of decisions for the traffic management departments.

2. Connotation and Measurement of Non-equilibrium Depth of Supply and Demand of City Transportation System

The non-equilibrium depth of supply and demand of city agglomeration transportation system is a quantitative description of relationship between the city and the city, inside of city and outside of the agglomeration. As the non-equilibrium depth varying with time is noted, gained by the total demand divided by the total supply, the non-equilibrium depth

of the three parts can be calculated respectively, and then combined with the relationship between them and other factors, the ultimate whole non-equilibrium depth can be obtained, the calculation formula is showed as follows.

k(t) = N(t)/D(t) (1)

Formula (1) is just a basic one for the whole calculation procedure of non-equilibrium depth of supply and demand, a more complicated calculation process is needed illustrated below.

2.1. Classification of non-equilibrium between supply and demand in city agglomeration transportation system

The definition of non-equilibrium depth of supply and demand in city agglomeration transportation system indicates that k = i, the relation between supply and demand keeps in equilibrium, or it will turn to be non-equilibrium. The non-equilibrium can be divided into the following three types.

1--Acceptable non-equilibrium [K.sub.a]

The equilibrium seems always ideal, normally the total supply and demand of city agglomeration stays in non-equilibrium all the time. However, it is acknowledged that none of any measures become necessary to take, when [absolute value of K] < [K.sub.a] . The city agglomeration transportation system, possessing varieties of transportation modes and corresponding infrastructure, can simultaneously devote itself to keep the whole system stable.

2--Mild non-equilibrium [K.sub.b]

With the non-equilibrium depth of supply and demand of city agglomeration transportation system increasing, the adjustment of system cannot afford to maintain its workings until [K.sub.a] < [absolute value of K] < [K.sub.b], and a number of mind and appropriate measures and demand management should be applied to keep the supply and demand balanced.

3--Severe non-equilibrium [K.sub.c]

When [K.sub.b] < [absolute value of k] < [K.sub.c], the city agglomeration transportation has become the bottleneck of the social and economic development, and then efforts should be reinforced by the government in strengthening the investment in the infrastructure construction of city agglomeration transportation system (such as increasing inter-city highways, railways and shipping routes), and trimming the overall layout of city agglomeration transportation system, containing modes of highway, railway, airlift, water transportation.

2.2. Assumptions and instructions

Assuming s = {[s.sub.1],[s.sub.2],[s.sub.3], ...,[s.sub.m][s.sub.m+1], ... [s.sub.n-1],[s.sub.n]}to be the collection of all cities in the chosen area, [s.sub.i] [??] [s.sub.j] is recognized as any city of this region, [s.sub.i] [??] [s.sub.j] [member of] S,. [G.sub.ij] and [N.sub.ij] represents the traffic capacity and traffic demand between [s.sub.i] and [s.sub.j], S' = {[s.sub.1],[s.sub.2],[s.sub.3], ..., [s.sub.m-1],[s.sub.m]} is an agglomeration of cities within S, S' [subset or equal to] S. Traffic capacity is shown as [G.sub.1] [??] [G.sub.2] [??] [G.sub.3], representing the capacity of the city inside, city to city and the agglomeration to the outside, similarly, [N.sub.1] [??] [N.sub.2] [??] [N.sub.3] represents the traffic demand of three parts, and [K.sub.1] [??] [K.sup.2] [??] K is for corresponding non-equilibrium depth respectively.

2.3. Non-equilibrium depth calculation of supply and demand

When [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] then the non-equilibrium depth of supply and demand inside of the cities K1 is figured in formula (2).

K = [summation over (i)] [summation over (j)][G.sub.ij]/[summation over (i)][summation over (j)][N.sub.ij] (2)

3. Methods

According to the definition of the total non-equilibrium depth of traffic demand and supply in the city agglomeration, the calculation method is shown as followings.

3.1. Restrained non-equilibrium

Restrained non-equilibrium is related to the traffic demand and traffic supply alone, which can be classified into the general and the dimensional based on the nonequilibrium calculation before.

General restrained non-equilibrium: the ratio of the overall traffic supply to the overall traffic demand ratio of the city agglomeration, showing as formula (3).

K = 1/3 ([G.sub.1]/[N.sub.1] + [G.sub.2]/[N.sub.2] + [G.sub.3]/[N.sub.3]) = 1/3([K.sub.1] + [K.sub.2] + [K.sub.3]) (3)

This kind of non-equilibrium depth calculation are too simple to illustrate the complexity of the relationship between supply and demand and the diversity of factors within city agglomeration transportation system, and it will result in wild inaccuracy easily, so the non-equilibrium in a general sense is put forward to be superior to restrained nonequilibrium.

3.2. Generalized non-equilibrium

By considering the time and transportation modes as well as the layout of city agglomeration transportation system, the generalized non-equilibrium depth is figured as followings.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

Based on the theory of restrained non-equilibrium, the generalized non-equilibrium expand it further, as shown in Figure 1. By conducting surface fitting to Figure 1, the three-dimensional structure of non-equilibrium can be determined in Figure 2.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

4. Results and Analysis

Assuming S = {[s.sub.1],[s.sub.2],[s.sub.3],[s.sub.4],[s.sub.5]} is a chosen area, [s.sub.1],[s.sub.2],[s.sub.3],[s.sub.4],[s.sub.5] are the cities within it, there is a city agglomeration S' = {[s.sub.1],[s.sub.2],[s.sub.3]}, S' [member of] S and the non-equilibrium depth of S' is calculated to verify the model above. Suppose the supply and demand development of S' is independent, the traffic demand for highway, railway, airlift and waterway inside of [s.sub.1],[s.sub.2],[s.sub.3] is 40000PCU/ h, 100000pcu /h, 0, 0 respectively, and the supply is 35000pcu / h, 15000pcu / h, 0, 0 ; Similarly the traffic demand between the cities for this four transportation modes is 100000pcu / h, 80000pcu / h, 50000pcu / h, 10000pcu / h, and the supply is 90000pcu / h, 85000pcu / h, 90000pcu / h, 10000pcu / h; the traffic demand outside of [s.sub.1],[s.sub.2],[s.sub.3], connecting with [s.sub.4][??], [s.sub.5] for this four transportation modes is i50000pcu / h, 120000pcu / h, 90000pm / h, 30000pcu / h respectively, and the supply is 180000pcu / h, 100000pcu / h, i00000pcu / h, 40000pcu / h ; Assuming the acceptable non-equilibrium depth of this agglomeration is 0.7 < K < 1.5, the mild non-equilibrium depth is 0.5 < K < 2, the severe non-equilibrium depth is 0.34 < K < 3.

The general restrained non-equilibrium depth of S' is:

The dimensional restrained non-equilibrium depth of S' is:

The generalized non-equilibrium depth of S' (shown in Figure 3) is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[FIGURE 3 OMITTED]

Then conducting the surface fitting, and calculation process, shown in figure 4.

[FIGURE 4 OMITTED]

5. Conclusions

By studying the calculation method of the non-equilibrium depth of urban agglomeration transportation system, two kinds of calculation methods are put forward-restrained non-equilibrium and generalized non-equilibrium. Non-equilibrium depths in parts of the city inside, city to city and the agglomeration to the outside are obtained respectively, and then based on their weight, the total non-equilibrium depth can be obtained, as well as its three-dimensional structure and the fitting surface, finally, the case analysis is used to verify this established model. By using this method, the non-equilibrium between supply and demand of urban agglomeration transportation system is analyzed quantitatively, which lay a solid foundation for the research on the non-equilibrium of supply and demand, providing theoretical and technical support for infrastructure construction of city agglomeration transportation.

Recebido/Submission: 09/04/2016

Aceitacao/Acceptance: 04/06/2016

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Chen Yao (1) *, Chengbing Li (2)

* yc811117ok@163.com

(1) College of Traffic and Transportation, Ludong University, Yantai, 264000, China

(2) School of Transportation, Inner Mongolia University, Hohhot, Inner Mongolia, 010070, China

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Author: | Yao, Chen; Li, Chengbing |
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Publication: | RISTI (Revista Iberica de Sistemas e Tecnologias de Informacao) |

Date: | Aug 1, 2016 |

Words: | 2186 |

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